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  • 1
    Electronic Resource
    Electronic Resource
    Some independence results related to the arc-sine law (1996)
    Springer
    Journal of theoretical probability 9 (1996), S. 447-458 
    Details
    ISSN: 1572-9230
    Keywords: Arc-sine law ; Lévy process ; local time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide proofs for recent results of Getoor and Sharpe on the distribution of local times on rays for certain planar Lévy processes which were invalidated by an appeal to an incorrect assertion. Our arguments rely on independence properties related to the arc-sine law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02214659
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  • 2
    Electronic Resource
    Electronic Resource
    Conditioning a reflected one-dimensional diffusion via its canonical decomposition (1993)
    Springer
    Journal of theoretical probability 6 (1993), S. 303-321 
    Details
    ISSN: 1572-9230
    Keywords: One-dimensional diffusion ; harmonic transform ; excursion ; zero-energy additive functional
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with a class of nonnegative reflected diffusionsX which have a canonical decompositionX=N-B, whereB is a Brownian motion andN a locally zero energy additive functional that decreases whenX〉0. We condition the diffusion by the event “N stays nonpositive”. This conditioned diffusion naturally appears in various circumstances. In particular, we present a simple pathwise construction of the conditioned process from the original diffusion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01047576
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  • 3
    Electronic Resource
    Electronic Resource
    Increase of stable processes (1994)
    Springer
    Journal of theoretical probability 7 (1994), S. 551-563 
    Details
    ISSN: 1572-9230
    Keywords: Stable process ; increase points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract One says thatt〉0 is an increase time for a real-valued path ω if ω stays above the level ω(t) immediately after timet, and below ω(t) immediately before timet. Dvoretzkyet al.,(10) proved that Brownian motion has no increase times a.s. This result is extended here to (strictly) stable processes. Specifically, the probability that a stable processX possesses increase times is 0 if and only ifP(X 1≥0)≤1/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02213568
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  • 4
    Electronic Resource
    Electronic Resource
    A Ratio Ergodic Theorem for Brownian Additive Functionals with Infinite Mean (1997)
    Springer
    Potential analysis 7 (1997), S. 615-621 
    Details
    ISSN: 1572-929X
    Keywords: Brownian motion ; additive functional ; ratio ergodic theorem ; spectral theory of strings.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We determine the asymptotic behaviour of the ratio of certain additive functionals of a linear Brownian motion, solving a problem raised by Erickson.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1017929801399
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  • 5
    Electronic Resource
    Electronic Resource
    Sample path behaviour in connection with generalized arcsine laws (1995)
    Springer
    Probability theory and related fields 103 (1995), S. 317-327 
    Details
    ISSN: 1432-2064
    Keywords: 60G17 ; 60J25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary LetG=(G(t),t≧0) be the process of last passage times at some fixed point of a Markov process. The Dynkin-Lamperti theorem provides a necessary and sufficient condition forG(t)/t to converge in law ast→∞ to some non-degenerate limit (which is then a generalized arcsine law). Under this condition, we give a simple integral test that characterizes the lower-functions ofG. We obtain a similar result forA +=(A + (t),t≧0), the time spent in [0, ∞) by a real-valued diffusion process, in connection with Watanabe's recent extension of Lévy's second arcsine law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195477
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  • 6
    Electronic Resource
    Electronic Resource
    Intersection of independent regenerative sets (1999)
    Springer
    Probability theory and related fields 114 (1999), S. 97-121 
    Details
    ISSN: 1432-2064
    Keywords: Mathematics Subject Classification (1991): 60J30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We investigate the nature of the intersection of two independent regenerative sets. The approach combines Bochners subordination and potential theory for a pair of Markov processes in duality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050223
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  • 7
    Electronic Resource
    Electronic Resource
    The Bolthausen–Sznitman coalescent and the genealogy of continuous-state branching processes (2000)
    Springer
    Probability theory and related fields 117 (2000), S. 249-266 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We use Bochner’s subordination to give a representation of the genealogical structure associated with general continuous-state branching processes. We then apply this representation to connections between a branching process introduced by Neveu, and the coalescent process recently investigated by Bolthausen-Sznitman and others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050006
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  • 8
    Electronic Resource
    Electronic Resource
    A fragmentation process connected to Brownian motion (2000)
    Springer
    Probability theory and related fields 117 (2000), S. 289-301 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Let (B s , s≥ 0) be a standard Brownian motion and T 1 its first passage time at level 1. For every t≥ 0, we consider ladder time set ℒ (t) of the Brownian motion with drift t, B (t) s = B s + ts, and the decreasing sequence F(t) = (F 1(t), F 2(t), …) of lengths of the intervals of the random partition of [0, T 1] induced by ℒ (t) . The main result of this work is that (F(t), t≥ 0) is a fragmentation process, in the sense that for 0 ≤t 〈 t′, F(t′) is obtained from F(t) by breaking randomly into pieces each component of F(t) according to a law that only depends on the length of this component, and independently of the others. We identify the fragmentation law with the one that appears in the construction of the standard additive coalescent by Aldous and Pitman [3].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050008
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  • 9
    Electronic Resource
    Electronic Resource
    Regenerative embedding of Markov sets (1997)
    Springer
    Probability theory and related fields 108 (1997), S. 559-571 
    Details
    ISSN: 1432-2064
    Keywords: Key words: Markov set ; Regenerative property ; Skorohod embedding ; Subordinator. ; Mathematics Subject Classification (1991): 60D05 ; 60J30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary.  Given a closed Markov (i.e. regenerative) set in [0,∞), we characterize the laws of the Markov sets which are regeneratively embedded into the latter. Typically, let Φ(1) and Φ(2) be two Laplace exponents corresponding to two regenerative laws, and M (2) a Markov set with exponent Φ(2). There exists a Markov set M (1) with exponent Φ(1) which is regeneratively embedded into M (2) if and only if Φ(1)/Φ(2) is a completely monotone function. Several examples and applications are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050121
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  • 10
    Electronic Resource
    Electronic Resource
    Excursions of a BES0 (d) and its drift term (0〈d〈1) (1990)
    Springer
    Probability theory and related fields 84 (1990), S. 231-250 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary LetX be a BES0(d) (0〈d〈1) with canonical decompositionX=B+(d−1)H, whereB is a brownian motion andH locally of zero energy. The process (X; H) is shown to have a local time at (0; 0), and the characteristic measure of its excursions (in Itô's sense) is described. This study leads us to new determinations of the-space variable-process defined by the occupation densities ofH taken at some optional times.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01197846
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